This invention relates generally to the field of direction finding techniques by which the angles-of-arrival of incident radiation are determined using an array of radiation-sensing elements. More particularly, the present invention relates to a method for the efficient and accurate determination of the phase ambiguity that takes the form of a whole number of full cycles that corrupt an interferometric measurement due to the differential path length between individual radiation detecting elements and a common source of electromagnetic radiation. The recovery of the unambiguous phase term permits the determination of the unambiguous angular direction to the radiation source.
Interferometric direction finding systems frequently use three or more sensing elements separated by fixed distances and a receiving network for determining the frequency and phase of the incident radiation. The elements may be part of either a RF antenna array or an acoustical array depending on whether a radar or sonar application is intended. An interferometric baseline is the shortest distance between sensing elements. Where the baseline is less than half a wavelength of the frequency of interest, the comparison of phase measurements permits the unambiguous determination of the angle from which the radiation or acoustical waveform originated in the propagation plane.
Where the baseline exceeds half the wavelength of the highest frequency, the interferometric phase measurement results in two or more possible angles-of-arrival. Such an ambiguity takes the form of an integer multiple of 2.pi. in the differential phase measurement because a realizable receiving system is incapable of determining phase angles beyond 360 degrees. Where a narrow-bandwidth system is used, the angular ambiguity can be avoided by making the system baseline less than a half wavelength of the highest frequency. In such a system, the accuracy is generally poor due to the presence of thermal noise that acts to lower the signal-to-noise ratio and accordingly degrades the accuracy of the angle-of-arrival measurement. Where greater accuracy is required or the system is wide-band, it is often necessary to increase the baseline. A wide baseline system is one in which the baseline is greater than one-half the wavelength of the signal. When applying a wide baseline system, one trades the increased accuracy against the necessity of distinguishing the resulting ambiguous angles-of-arrival that are the natural products of sensing elements spaced apart by several multiples of the wavelength of the signal.
The relevant prior art methods used for resolving angular ambiguities appear to be U.S. Pat. No. 5,218,361 to Avila and U.S. Pat. No. 5,296,861 to Knight. U.S. Pat. No. 5,218,361 to Avila uses spatial changes in the antenna element orientation by rotating the interferometric antenna array. The rotation of the array is necessary to acquire phase data at multiple orientations in order to construct a simultaneous set of equations. Where the phase data are acquired by successive measurements at a rate that yields a system of equations wherein each equation is a function of the same ambiguity number, the system of equations can be combined to eliminate the dependence on the ambiguity number and thus the unambiguous angles-of-arrival can be determined. In contrast to Avila, the present invention uses a plurality of antenna elements in a fixed configuration and orientation relative to the signal source whereby the ambiguity may be determined instantaneously over a full range of array orientations without the need to rotate the array. Furthermore, the present invention has the additional advantage that the phase data need not necessarily be restricted in such ways as to require that each phase measurement be a function of the same ambiguity number.
U.S. Pat. No. 5,296,861 to Knight applies the maximum likelihood estimation techniques to the relative phases of GPS carrier signals so as to derive the attitude angles of receiving platforms and resolves GPS carriers relative phases ambiguities with integer programming branch and bound techniques. The Knight platform attitude solution using GPS is the inverse of the emitter angle of arrival problem of interest in direction finding. The platform attitude problem is characterized by multiple emitters of exactly known positions. The Direction Finding problem handles separate emitters as separate concerns. The ambiguously measured angle between the baselines and the AOA from the emitter/satellites is a common feature. In DF the unambiguous measured angle is the final output, whereas in the platform attitude measurement it is only a means to an end.
The preceding discussion provides motivation for the appreciable need of a method for the correction of the ambiguity in the determining of the angular position of a source of electromagnetic radiation. In overcoming the limitations of the prior art, the present invention fulfills the need for a closed-form solution that is both computationally efficient and robust, providing accurate results in the presence of noise.